3.27.80 \(\int \frac {12 x-12 x^2-12 x^3+24 x^4-12 x^5+(-12+12 x+24 x^2-48 x^3+24 x^4) \log (2)+(-12 x+24 x^2-12 x^3) \log ^2(2)+(-16+44 x-40 x^2+44 x^3-40 x^4+12 x^5+(-16+44 x-88 x^2+80 x^3-24 x^4) \log (2)+(-16+44 x-40 x^2+12 x^3) \log ^2(2)) \log (\frac {1}{2} (4-3 x))}{(-4 x^2+11 x^3-10 x^4+3 x^5+(8 x-22 x^2+20 x^3-6 x^4) \log (2)+(-4+11 x-10 x^2+3 x^3) \log ^2(2)) \log ^2(\frac {1}{2} (4-3 x))} \, dx\) [2680]

Optimal. Leaf size=34 \[ \frac {4 \left (x-\frac {x}{\left (-x+x^2\right ) (-x+\log (2))}\right )}{\log \left (2-\frac {3 x}{2}\right )} \]

[Out]

4*(x-x/(ln(2)-x)/(x^2-x))/ln(2-3/2*x)

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Rubi [F]
time = 3.85, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {12 x-12 x^2-12 x^3+24 x^4-12 x^5+\left (-12+12 x+24 x^2-48 x^3+24 x^4\right ) \log (2)+\left (-12 x+24 x^2-12 x^3\right ) \log ^2(2)+\left (-16+44 x-40 x^2+44 x^3-40 x^4+12 x^5+\left (-16+44 x-88 x^2+80 x^3-24 x^4\right ) \log (2)+\left (-16+44 x-40 x^2+12 x^3\right ) \log ^2(2)\right ) \log \left (\frac {1}{2} (4-3 x)\right )}{\left (-4 x^2+11 x^3-10 x^4+3 x^5+\left (8 x-22 x^2+20 x^3-6 x^4\right ) \log (2)+\left (-4+11 x-10 x^2+3 x^3\right ) \log ^2(2)\right ) \log ^2\left (\frac {1}{2} (4-3 x)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(12*x - 12*x^2 - 12*x^3 + 24*x^4 - 12*x^5 + (-12 + 12*x + 24*x^2 - 48*x^3 + 24*x^4)*Log[2] + (-12*x + 24*x
^2 - 12*x^3)*Log[2]^2 + (-16 + 44*x - 40*x^2 + 44*x^3 - 40*x^4 + 12*x^5 + (-16 + 44*x - 88*x^2 + 80*x^3 - 24*x
^4)*Log[2] + (-16 + 44*x - 40*x^2 + 12*x^3)*Log[2]^2)*Log[(4 - 3*x)/2])/((-4*x^2 + 11*x^3 - 10*x^4 + 3*x^5 + (
8*x - 22*x^2 + 20*x^3 - 6*x^4)*Log[2] + (-4 + 11*x - 10*x^2 + 3*x^3)*Log[2]^2)*Log[(4 - 3*x)/2]^2),x]

[Out]

(-4*(4 - 3*x))/(3*Log[2 - (3*x)/2]) + (4*(43 - 108*Log[2]^2 - Log[4096] + Log[16]*Log[134217728]))/(3*(4 - Log
[8])*Log[2 - (3*x)/2]) + (4*(3 - 12*Log[2]^2 + Log[8]*Log[16])*Defer[Int][1/((-1 + x)*Log[2 - (3*x)/2]^2), x])
/(1 - Log[2]) - (12*(1 - 8*Log[2]^2 + Log[4]*Log[16])*Defer[Int][1/((x - Log[2])*Log[2 - (3*x)/2]^2), x])/((1
- Log[2])*(4 - Log[8])) - (4*Defer[Int][1/((-1 + x)^2*Log[2 - (3*x)/2]), x])/(1 - Log[2]) + (4*Defer[Int][1/((
x - Log[2])^2*Log[2 - (3*x)/2]), x])/(1 - Log[2])

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \left (3 x^5+\log (8)-x \left (3-3 \log ^2(2)+\log (8)\right )+3 x^3 \left (1+\log ^2(2)+\log (16)\right )-x^4 (6+\log (64))-x^2 \left (-3+6 \log ^2(2)+\log (64)\right )-(-4+3 x) \left (1+x^4+\log (2)+\log ^2(2)-2 x^3 (1+\log (2))-2 x \left (1+\log (2)+\log ^2(2)\right )+x^2 \left (1+\log ^2(2)+\log (16)\right )\right ) \log \left (2-\frac {3 x}{2}\right )\right )}{(4-3 x) (1-x)^2 (x-\log (2))^2 \log ^2\left (2-\frac {3 x}{2}\right )} \, dx\\ &=4 \int \frac {3 x^5+\log (8)-x \left (3-3 \log ^2(2)+\log (8)\right )+3 x^3 \left (1+\log ^2(2)+\log (16)\right )-x^4 (6+\log (64))-x^2 \left (-3+6 \log ^2(2)+\log (64)\right )-(-4+3 x) \left (1+x^4+\log (2)+\log ^2(2)-2 x^3 (1+\log (2))-2 x \left (1+\log (2)+\log ^2(2)\right )+x^2 \left (1+\log ^2(2)+\log (16)\right )\right ) \log \left (2-\frac {3 x}{2}\right )}{(4-3 x) (1-x)^2 (x-\log (2))^2 \log ^2\left (2-\frac {3 x}{2}\right )} \, dx\\ &=4 \int \left (\frac {3 x^5-6 x^4 (1+\log (2))-3 x (1-(-1+\log (2)) \log (2))+3 x^2 \left (1-2 \log ^2(2)-\log (4)\right )+\log (8)+3 x^3 \left (1+\log ^2(2)+\log (16)\right )}{(4-3 x) (1-x)^2 (x-\log (2))^2 \log ^2\left (2-\frac {3 x}{2}\right )}+\frac {1+x^4+\log (2)+\log ^2(2)-2 x^3 (1+\log (2))-2 x \left (1+\log (2)+\log ^2(2)\right )+x^2 \left (1+\log ^2(2)+\log (16)\right )}{(1-x)^2 (x-\log (2))^2 \log \left (2-\frac {3 x}{2}\right )}\right ) \, dx\\ &=4 \int \frac {3 x^5-6 x^4 (1+\log (2))-3 x (1-(-1+\log (2)) \log (2))+3 x^2 \left (1-2 \log ^2(2)-\log (4)\right )+\log (8)+3 x^3 \left (1+\log ^2(2)+\log (16)\right )}{(4-3 x) (1-x)^2 (x-\log (2))^2 \log ^2\left (2-\frac {3 x}{2}\right )} \, dx+4 \int \frac {1+x^4+\log (2)+\log ^2(2)-2 x^3 (1+\log (2))-2 x \left (1+\log (2)+\log ^2(2)\right )+x^2 \left (1+\log ^2(2)+\log (16)\right )}{(1-x)^2 (x-\log (2))^2 \log \left (2-\frac {3 x}{2}\right )} \, dx\\ &=4 \int \left (\frac {1}{\log \left (2-\frac {3 x}{2}\right )}+\frac {1}{(-1+x)^2 (-1+\log (2)) \log \left (2-\frac {3 x}{2}\right )}+\frac {1-\log (2)-4 \log ^3(2)+\log ^2(2) \log (16)}{(x-\log (2))^2 (-1+\log (2))^2 \log \left (2-\frac {3 x}{2}\right )}\right ) \, dx+4 \int \frac {-3 x^4+9 \log (2)+x^3 (3+6 \log (2))+3 \log (4)+x^2 \left (6 \log (2)-3 \log ^2(2)-3 \log (16)\right )+x \left (-3+6 \log (2)+3 \log ^2(2)+3 \log (4)-3 \log (16)\right )-3 \log (16)}{(4-3 x) (1-x) (x-\log (2))^2 \log ^2\left (2-\frac {3 x}{2}\right )} \, dx\\ &=4 \int \frac {-3-3 x^3+6 \log (2)+12 \log ^2(2)+x^2 (3+3 \log (2))+3 \log (4)+x (9 \log (2)-3 \log (16))-3 \log (16)-3 \log (2) \log (16)}{(4-3 x) (1-x) (x-\log (2)) \log ^2\left (2-\frac {3 x}{2}\right )} \, dx+4 \int \frac {1}{\log \left (2-\frac {3 x}{2}\right )} \, dx-\frac {4 \int \frac {1}{(-1+x)^2 \log \left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}+\frac {4 \int \frac {1}{(x-\log (2))^2 \log \left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}\\ &=-\left (\frac {8}{3} \text {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,2-\frac {3 x}{2}\right )\right )+4 \int \left (-\frac {1}{\log ^2\left (2-\frac {3 x}{2}\right )}+\frac {3 \left (-1+8 \log ^2(2)-\log (4) \log (16)\right )}{(x-\log (2)) (-1+\log (2)) (-4+\log (8)) \log ^2\left (2-\frac {3 x}{2}\right )}+\frac {-3+12 \log ^2(2)-\log (8) \log (16)}{(-1+x) (-1+\log (2)) \log ^2\left (2-\frac {3 x}{2}\right )}+\frac {43-108 \log ^2(2)-\log (4096)+\log (16) \log (134217728)}{(-4+3 x) (-4+\log (8)) \log ^2\left (2-\frac {3 x}{2}\right )}\right ) \, dx-\frac {4 \int \frac {1}{(-1+x)^2 \log \left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}+\frac {4 \int \frac {1}{(x-\log (2))^2 \log \left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}\\ &=-\frac {8}{3} \text {li}\left (2-\frac {3 x}{2}\right )-4 \int \frac {1}{\log ^2\left (2-\frac {3 x}{2}\right )} \, dx-\frac {4 \int \frac {1}{(-1+x)^2 \log \left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}+\frac {4 \int \frac {1}{(x-\log (2))^2 \log \left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}-\frac {\left (12 \left (1-8 \log ^2(2)+\log (4) \log (16)\right )\right ) \int \frac {1}{(x-\log (2)) \log ^2\left (2-\frac {3 x}{2}\right )} \, dx}{(1-\log (2)) (4-\log (8))}+\frac {\left (4 \left (3-12 \log ^2(2)+\log (8) \log (16)\right )\right ) \int \frac {1}{(-1+x) \log ^2\left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}-\frac {\left (4 \left (43-108 \log ^2(2)-\log (4096)+\log (16) \log (134217728)\right )\right ) \int \frac {1}{(-4+3 x) \log ^2\left (2-\frac {3 x}{2}\right )} \, dx}{4-\log (8)}\\ &=-\frac {8}{3} \text {li}\left (2-\frac {3 x}{2}\right )+\frac {8}{3} \text {Subst}\left (\int \frac {1}{\log ^2(x)} \, dx,x,2-\frac {3 x}{2}\right )-\frac {4 \int \frac {1}{(-1+x)^2 \log \left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}+\frac {4 \int \frac {1}{(x-\log (2))^2 \log \left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}-\frac {\left (12 \left (1-8 \log ^2(2)+\log (4) \log (16)\right )\right ) \int \frac {1}{(x-\log (2)) \log ^2\left (2-\frac {3 x}{2}\right )} \, dx}{(1-\log (2)) (4-\log (8))}+\frac {\left (4 \left (3-12 \log ^2(2)+\log (8) \log (16)\right )\right ) \int \frac {1}{(-1+x) \log ^2\left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}+\frac {\left (8 \left (43-108 \log ^2(2)-\log (4096)+\log (16) \log (134217728)\right )\right ) \text {Subst}\left (\int -\frac {1}{2 x \log ^2(x)} \, dx,x,2-\frac {3 x}{2}\right )}{3 (4-\log (8))}\\ &=-\frac {4 (4-3 x)}{3 \log \left (2-\frac {3 x}{2}\right )}-\frac {8}{3} \text {li}\left (2-\frac {3 x}{2}\right )+\frac {8}{3} \text {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,2-\frac {3 x}{2}\right )-\frac {4 \int \frac {1}{(-1+x)^2 \log \left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}+\frac {4 \int \frac {1}{(x-\log (2))^2 \log \left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}-\frac {\left (12 \left (1-8 \log ^2(2)+\log (4) \log (16)\right )\right ) \int \frac {1}{(x-\log (2)) \log ^2\left (2-\frac {3 x}{2}\right )} \, dx}{(1-\log (2)) (4-\log (8))}+\frac {\left (4 \left (3-12 \log ^2(2)+\log (8) \log (16)\right )\right ) \int \frac {1}{(-1+x) \log ^2\left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}-\frac {\left (4 \left (43-108 \log ^2(2)-\log (4096)+\log (16) \log (134217728)\right )\right ) \text {Subst}\left (\int \frac {1}{x \log ^2(x)} \, dx,x,2-\frac {3 x}{2}\right )}{3 (4-\log (8))}\\ &=-\frac {4 (4-3 x)}{3 \log \left (2-\frac {3 x}{2}\right )}-\frac {4 \int \frac {1}{(-1+x)^2 \log \left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}+\frac {4 \int \frac {1}{(x-\log (2))^2 \log \left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}-\frac {\left (12 \left (1-8 \log ^2(2)+\log (4) \log (16)\right )\right ) \int \frac {1}{(x-\log (2)) \log ^2\left (2-\frac {3 x}{2}\right )} \, dx}{(1-\log (2)) (4-\log (8))}+\frac {\left (4 \left (3-12 \log ^2(2)+\log (8) \log (16)\right )\right ) \int \frac {1}{(-1+x) \log ^2\left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}-\frac {\left (4 \left (43-108 \log ^2(2)-\log (4096)+\log (16) \log (134217728)\right )\right ) \text {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log \left (2-\frac {3 x}{2}\right )\right )}{3 (4-\log (8))}\\ &=-\frac {4 (4-3 x)}{3 \log \left (2-\frac {3 x}{2}\right )}+\frac {4 \left (43-108 \log ^2(2)-\log (4096)+\log (16) \log (134217728)\right )}{3 (4-\log (8)) \log \left (2-\frac {3 x}{2}\right )}-\frac {4 \int \frac {1}{(-1+x)^2 \log \left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}+\frac {4 \int \frac {1}{(x-\log (2))^2 \log \left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}-\frac {\left (12 \left (1-8 \log ^2(2)+\log (4) \log (16)\right )\right ) \int \frac {1}{(x-\log (2)) \log ^2\left (2-\frac {3 x}{2}\right )} \, dx}{(1-\log (2)) (4-\log (8))}+\frac {\left (4 \left (3-12 \log ^2(2)+\log (8) \log (16)\right )\right ) \int \frac {1}{(-1+x) \log ^2\left (2-\frac {3 x}{2}\right )} \, dx}{1-\log (2)}\\ \end {aligned} \end {gather*}

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Mathematica [F]
time = 1.59, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {12 x-12 x^2-12 x^3+24 x^4-12 x^5+\left (-12+12 x+24 x^2-48 x^3+24 x^4\right ) \log (2)+\left (-12 x+24 x^2-12 x^3\right ) \log ^2(2)+\left (-16+44 x-40 x^2+44 x^3-40 x^4+12 x^5+\left (-16+44 x-88 x^2+80 x^3-24 x^4\right ) \log (2)+\left (-16+44 x-40 x^2+12 x^3\right ) \log ^2(2)\right ) \log \left (\frac {1}{2} (4-3 x)\right )}{\left (-4 x^2+11 x^3-10 x^4+3 x^5+\left (8 x-22 x^2+20 x^3-6 x^4\right ) \log (2)+\left (-4+11 x-10 x^2+3 x^3\right ) \log ^2(2)\right ) \log ^2\left (\frac {1}{2} (4-3 x)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(12*x - 12*x^2 - 12*x^3 + 24*x^4 - 12*x^5 + (-12 + 12*x + 24*x^2 - 48*x^3 + 24*x^4)*Log[2] + (-12*x
+ 24*x^2 - 12*x^3)*Log[2]^2 + (-16 + 44*x - 40*x^2 + 44*x^3 - 40*x^4 + 12*x^5 + (-16 + 44*x - 88*x^2 + 80*x^3
- 24*x^4)*Log[2] + (-16 + 44*x - 40*x^2 + 12*x^3)*Log[2]^2)*Log[(4 - 3*x)/2])/((-4*x^2 + 11*x^3 - 10*x^4 + 3*x
^5 + (8*x - 22*x^2 + 20*x^3 - 6*x^4)*Log[2] + (-4 + 11*x - 10*x^2 + 3*x^3)*Log[2]^2)*Log[(4 - 3*x)/2]^2),x]

[Out]

Integrate[(12*x - 12*x^2 - 12*x^3 + 24*x^4 - 12*x^5 + (-12 + 12*x + 24*x^2 - 48*x^3 + 24*x^4)*Log[2] + (-12*x
+ 24*x^2 - 12*x^3)*Log[2]^2 + (-16 + 44*x - 40*x^2 + 44*x^3 - 40*x^4 + 12*x^5 + (-16 + 44*x - 88*x^2 + 80*x^3
- 24*x^4)*Log[2] + (-16 + 44*x - 40*x^2 + 12*x^3)*Log[2]^2)*Log[(4 - 3*x)/2])/((-4*x^2 + 11*x^3 - 10*x^4 + 3*x
^5 + (8*x - 22*x^2 + 20*x^3 - 6*x^4)*Log[2] + (-4 + 11*x - 10*x^2 + 3*x^3)*Log[2]^2)*Log[(4 - 3*x)/2]^2), x]

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(71\) vs. \(2(32)=64\).
time = 4.48, size = 72, normalized size = 2.12

method	result	size
norman	\(\frac {-4+\left (4 \ln \left (2\right )+4\right ) x^{2}-4 x^{3}-4 x \ln \left (2\right )}{\left (x -1\right ) \left (\ln \left (2\right )-x \right ) \ln \left (2-\frac {3 x}{2}\right )}\)	\(45\)
risch	\(\frac {4 x^{2} \ln \left (2\right )-4 x^{3}-4 x \ln \left (2\right )+4 x^{2}-4}{\left (x \ln \left (2\right )-x^{2}-\ln \left (2\right )+x \right ) \ln \left (2-\frac {3 x}{2}\right )}\)	\(49\)
default	\(\frac {\frac {4 \left (4-3 x \right )^{3}}{3}+\frac {4 \left (3 \ln \left (2\right )-9\right ) \left (4-3 x \right )^{2}}{3}+\frac {4 \left (-15 \ln \left (2\right )+24\right ) \left (4-3 x \right )}{3}-\frac {172}{3}+16 \ln \left (2\right )}{\left (-3 x +3\right ) \left (3 \ln \left (2\right )-3 x \right ) \left (\ln \left (2\right )-\ln \left (4-3 x \right )\right )}\)	\(72\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((12*x^3-40*x^2+44*x-16)*ln(2)^2+(-24*x^4+80*x^3-88*x^2+44*x-16)*ln(2)+12*x^5-40*x^4+44*x^3-40*x^2+44*x-1
6)*ln(2-3/2*x)+(-12*x^3+24*x^2-12*x)*ln(2)^2+(24*x^4-48*x^3+24*x^2+12*x-12)*ln(2)-12*x^5+24*x^4-12*x^3-12*x^2+
12*x)/((3*x^3-10*x^2+11*x-4)*ln(2)^2+(-6*x^4+20*x^3-22*x^2+8*x)*ln(2)+3*x^5-10*x^4+11*x^3-4*x^2)/ln(2-3/2*x)^2
,x,method=_RETURNVERBOSE)

[Out]

4/3*((4-3*x)^3+(3*ln(2)-9)*(4-3*x)^2+(-15*ln(2)+24)*(4-3*x)-43+12*ln(2))/(-3*x+3)/(3*ln(2)-3*x)/(ln(2)-ln(4-3*
x))

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 64 vs. \(2 (31) = 62\).
time = 0.53, size = 64, normalized size = 1.88 \begin {gather*} -\frac {4 \, {\left (x^{3} - x^{2} {\left (\log \left (2\right ) + 1\right )} + x \log \left (2\right ) + 1\right )}}{x^{2} \log \left (2\right ) - {\left (\log \left (2\right )^{2} + \log \left (2\right )\right )} x + \log \left (2\right )^{2} - {\left (x^{2} - x {\left (\log \left (2\right ) + 1\right )} + \log \left (2\right )\right )} \log \left (-3 \, x + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((12*x^3-40*x^2+44*x-16)*log(2)^2+(-24*x^4+80*x^3-88*x^2+44*x-16)*log(2)+12*x^5-40*x^4+44*x^3-40*x^
2+44*x-16)*log(2-3/2*x)+(-12*x^3+24*x^2-12*x)*log(2)^2+(24*x^4-48*x^3+24*x^2+12*x-12)*log(2)-12*x^5+24*x^4-12*
x^3-12*x^2+12*x)/((3*x^3-10*x^2+11*x-4)*log(2)^2+(-6*x^4+20*x^3-22*x^2+8*x)*log(2)+3*x^5-10*x^4+11*x^3-4*x^2)/
log(2-3/2*x)^2,x, algorithm="maxima")

[Out]

-4*(x^3 - x^2*(log(2) + 1) + x*log(2) + 1)/(x^2*log(2) - (log(2)^2 + log(2))*x + log(2)^2 - (x^2 - x*(log(2) +
1) + log(2))*log(-3*x + 4))

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Fricas [A]
time = 0.36, size = 47, normalized size = 1.38 \begin {gather*} \frac {4 \, {\left (x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (2\right ) + 1\right )}}{{\left (x^{2} - {\left (x - 1\right )} \log \left (2\right ) - x\right )} \log \left (-\frac {3}{2} \, x + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((12*x^3-40*x^2+44*x-16)*log(2)^2+(-24*x^4+80*x^3-88*x^2+44*x-16)*log(2)+12*x^5-40*x^4+44*x^3-40*x^
2+44*x-16)*log(2-3/2*x)+(-12*x^3+24*x^2-12*x)*log(2)^2+(24*x^4-48*x^3+24*x^2+12*x-12)*log(2)-12*x^5+24*x^4-12*
x^3-12*x^2+12*x)/((3*x^3-10*x^2+11*x-4)*log(2)^2+(-6*x^4+20*x^3-22*x^2+8*x)*log(2)+3*x^5-10*x^4+11*x^3-4*x^2)/
log(2-3/2*x)^2,x, algorithm="fricas")

[Out]

4*(x^3 - x^2 - (x^2 - x)*log(2) + 1)/((x^2 - (x - 1)*log(2) - x)*log(-3/2*x + 2))

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Sympy [A]
time = 0.13, size = 48, normalized size = 1.41 \begin {gather*} \frac {4 x^{3} - 4 x^{2} - 4 x^{2} \log {\left (2 \right )} + 4 x \log {\left (2 \right )} + 4}{\left (x^{2} - x - x \log {\left (2 \right )} + \log {\left (2 \right )}\right ) \log {\left (2 - \frac {3 x}{2} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((12*x**3-40*x**2+44*x-16)*ln(2)**2+(-24*x**4+80*x**3-88*x**2+44*x-16)*ln(2)+12*x**5-40*x**4+44*x**
3-40*x**2+44*x-16)*ln(2-3/2*x)+(-12*x**3+24*x**2-12*x)*ln(2)**2+(24*x**4-48*x**3+24*x**2+12*x-12)*ln(2)-12*x**
5+24*x**4-12*x**3-12*x**2+12*x)/((3*x**3-10*x**2+11*x-4)*ln(2)**2+(-6*x**4+20*x**3-22*x**2+8*x)*ln(2)+3*x**5-1
0*x**4+11*x**3-4*x**2)/ln(2-3/2*x)**2,x)

[Out]

(4*x**3 - 4*x**2 - 4*x**2*log(2) + 4*x*log(2) + 4)/((x**2 - x - x*log(2) + log(2))*log(2 - 3*x/2))

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Giac [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((12*x^3-40*x^2+44*x-16)*log(2)^2+(-24*x^4+80*x^3-88*x^2+44*x-16)*log(2)+12*x^5-40*x^4+44*x^3-40*x^
2+44*x-16)*log(2-3/2*x)+(-12*x^3+24*x^2-12*x)*log(2)^2+(24*x^4-48*x^3+24*x^2+12*x-12)*log(2)-12*x^5+24*x^4-12*
x^3-12*x^2+12*x)/((3*x^3-10*x^2+11*x-4)*log(2)^2+(-6*x^4+20*x^3-22*x^2+8*x)*log(2)+3*x^5-10*x^4+11*x^3-4*x^2)/
log(2-3/2*x)^2,x, algorithm="giac")

[Out]

Timed out

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Mupad [B]
time = 5.24, size = 2500, normalized size = 73.53 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((12*x + log(2 - (3*x)/2)*(44*x - log(2)*(88*x^2 - 44*x - 80*x^3 + 24*x^4 + 16) + log(2)^2*(44*x - 40*x^2 +
12*x^3 - 16) - 40*x^2 + 44*x^3 - 40*x^4 + 12*x^5 - 16) + log(2)*(12*x + 24*x^2 - 48*x^3 + 24*x^4 - 12) - log(
2)^2*(12*x - 24*x^2 + 12*x^3) - 12*x^2 - 12*x^3 + 24*x^4 - 12*x^5)/(log(2 - (3*x)/2)^2*(log(2)*(8*x - 22*x^2 +
20*x^3 - 6*x^4) + log(2)^2*(11*x - 10*x^2 + 3*x^3 - 4) - 4*x^2 + 11*x^3 - 10*x^4 + 3*x^5)),x)

[Out]

4*x - ((4*(x*log(2) - x^2*log(2) - x^2 + x^3 + 1))/(x - log(2) + x*log(2) - x^2) + (4*log(2 - (3*x)/2)*(3*x -
4)*(log(2) - 2*x + x^2*log(2)^2 - 2*x*log(2) - 2*x*log(2)^2 + 4*x^2*log(2) - 2*x^3*log(2) + log(2)^2 + x^2 - 2
*x^3 + x^4 + 1))/(3*(x^2*log(2)^2 - 2*x*log(2) - 2*x*log(2)^2 + 4*x^2*log(2) - 2*x^3*log(2) + log(2)^2 + x^2 -
2*x^3 + x^4)))/log(2 - (3*x)/2) + symsum(log(4391387136*log(512) - 29829980160*log(2) - root(266783382*z^5*lo
g(2)^12*log(512)^3 - 211631616*z^5*log(2)^8*log(512)^4 - 178682274*z^5*log(2)^9*log(512)^4 - 125892468*z^5*log
(2)^6*log(512)^4 + 123294312*z^5*log(2)^6*log(512)^3 + 68221278*z^5*log(2)^7*log(512)^4 - 52278048*z^5*log(2)^
10*log(512)^4 + 38263752*z^5*log(2)^14*log(512)^2 + 29760696*z^5*log(2)^15*log(512)^2 - 29760696*z^5*log(2)^6*
log(512)^2 + 26985393*z^5*log(2)^11*log(512)^4 - 17006112*z^5*log(2)^13*log(512)^3 - 12837690*z^5*log(2)^6*log
(512)^5 + 6613488*z^5*log(2)^5*log(512)^4 - 5821794*z^5*log(2)^9*log(512)^5 - 4776408*z^5*log(2)^8*log(512)^5
- 3418281*z^5*log(2)^10*log(512)^5 - 34362443619*z^5*log(2)^9*log(512)^2 + 2230740*z^5*log(2)^5*log(512)^5 + 1
653372*z^5*log(2)^12*log(512)^4 - 1076004*z^5*log(2)^4*log(512)^5 + 944784*z^5*log(2)^14*log(512)^3 - 944784*z
^5*log(2)^5*log(512)^3 - 761076*z^5*log(2)^7*log(512)^5 + 373977*z^5*log(2)^5*log(512)^6 - 288684*z^5*log(2)^1
3*log(512)^4 + 288684*z^5*log(2)^4*log(512)^4 + 258066*z^5*log(2)^8*log(512)^6 + 238383*z^5*log(2)^7*log(512)^
6 + 104976*z^5*log(2)^9*log(512)^6 - 74358*z^5*log(2)^6*log(512)^6 - 61236*z^5*log(2)^4*log(512)^6 - 52488*z^5
*log(2)^11*log(512)^5 + 34992*z^5*log(2)^3*log(512)^6 + 13122*z^5*log(2)^5*log(512)^7 + 11664*z^5*log(2)^12*lo
g(512)^5 - 11664*z^5*log(2)^3*log(512)^5 + 4131*z^5*log(2)^6*log(512)^7 + 3888*z^5*log(2)^3*log(512)^7 + 243*z
^5*log(2)^4*log(512)^7 + 108*z^5*log(2)^3*log(512)^8 - 34096191678*z^5*log(2)^12*log(512)^2 + 361936830168*z^5
*log(2)^11*log(512) + 198474081624*z^5*log(2)^10*log(512) + 176807232054*z^5*log(2)^13*log(512) + 344373768*z^
5*log(2)^15*log(512) - 306110016*z^5*log(2)^16*log(512) + 306110016*z^5*log(2)^7*log(512) + 34566516963*z^5*lo
g(2)^14*log(512) + 2835060588*z^5*log(2)^11*log(512)^3 + 2725229448*z^5*log(2)^7*log(512)^3 + 330684910722*z^5
*log(2)^12*log(512) + 133100461332*z^5*log(2)^9*log(512) - 2142770112*z^5*log(2)^7*log(512)^2 - 70816639014*z^
5*log(2)^10*log(512)^2 + 2077048575*z^5*log(2)^8*log(512)^3 + 12225268764*z^5*log(2)^8*log(512) + 6306078906*z
^5*log(2)^9*log(512)^3 - 27454242060*z^5*log(2)^8*log(512)^2 + 5877206019*z^5*log(2)^10*log(512)^3 - 572999686
2*z^5*log(2)^13*log(512)^2 - 65607985773*z^5*log(2)^11*log(512)^2 - 708204653892*z^5*log(2)^12 - 72447631443*z
^5*log(2)^15 - 252598158828*z^5*log(2)^10 - 24794911296*z^5*log(2)^9 - 411182278992*z^5*log(2)^11 - 3466121974
92*z^5*log(2)^14 - 638468965872*z^5*log(2)^13 - 1549681956*z^5*log(2)^16 + 860934420*z^5*log(2)^17 - 860934420
*z^5*log(2)^8 - 774932832*z^4*log(2)^8*log(512)^3 + 613637208*z^4*log(2)^12*log(512)^2 + 571699296*z^4*log(2)^
9*log(512)^3 + 532018368*z^4*log(2)^7*log(512)^3 + 319336992*z^4*log(2)^6*log(512)^2 - 286094592*z^4*log(2)^6*
log(512)^3 - 4568975424*z^4*log(2)^11*log(512)^2 + 266639040*z^4*log(2)^10*log(512)^3 - 245433888*z^4*log(2)^1
2*log(512)^3 - 72223488*z^4*log(2)^11*log(512)^3 + 54330912*z^4*log(2)^7*log(512)^4 - 37663056*z^4*log(2)^6*lo
g(512)^4 - 29160000*z^4*log(2)^8*log(512)^4 - 13226976*z^4*log(2)^15*log(512)^2 + 9346752*z^4*log(2)^5*log(512
)^4 - 6284952*z^4*log(2)^12*log(512)^4 + 5942808*z^4*log(2)^10*log(512)^4 + 5808672*z^4*log(2)^13*log(512)^3 +
4129056*z^4*log(2)^14*log(512)^3 + 3720816*z^4*log(2)^11*log(512)^4 - 2006208*z^4*log(2)^6*log(512)^5 - 19673
28*z^4*log(2)^4*log(512)^4 + 1936224*z^4*log(2)^9*log(512)^4 - 1889568*z^4*log(2)^16*log(512)^2 + 1889568*z^4*
log(2)^5*log(512)^2 - 1609632*z^4*log(2)^5*log(512)^3 + 1527984*z^4*log(2)^7*log(512)^5 + 1259712*z^4*log(2)^5
*log(512)^5 - 664848*z^4*log(2)^8*log(512)^5 - 489888*z^4*log(2)^15*log(512)^3 + 489888*z^4*log(2)^4*log(512)^
3 - 361584*z^4*log(2)^9*log(512)^5 + 279936*z^4*log(2)^11*log(512)^5 - 256608*z^4*log(2)^4*log(512)^5 - 202176
*z^4*log(2)^13*log(512)^4 + 128304*z^4*log(2)^10*log(512)^5 + 93312*z^4*log(2)^3*log(512)^5 - 55728*z^4*log(2)
^6*log(512)^6 + 38880*z^4*log(2)^5*log(512)^6 + 31104*z^4*log(2)^14*log(512)^4 - 31104*z^4*log(2)^3*log(512)^4
- 17496*z^4*log(2)^4*log(512)^6 + 12960*z^4*log(2)^7*log(512)^6 + 11016*z^4*log(2)^8*log(512)^6 + 10368*z^4*l
og(2)^3*log(512)^6 - 576*z^4*log(2)^4*log(512)^7 + 288*z^4*log(2)^5*log(512)^7 + 288*z^4*log(2)^3*log(512)^7 +
4032338112*z^4*log(2)^7*log(512)^2 + 14166091296*z^4*log(2)^9*log(512) + 3883062240*z^4*log(2)^13*log(512)^2
- 3878810712*z^4*log(2)^8*log(512)^2 - 7275781584*z^4*log(2)^10*log(512)^2 - 175729824*z^4*log(2)^16*log(512)
+ 62355744*z^4*log(2)^17*log(512) - 62355744*z^4*log(2)^6*log(512) - 25571523744*z^4*log(2)^8*log(512) - 25313
597712*z^4*log(2)^14*log(512) - 7692431328*z^4*log(2)^15*log(512) + 6031501056*z^4*log(2)^9*log(512)^2 + 29020
930128*z^4*log(2)^12*log(512) - 24505807392*z^4...

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